Banked Frictionless Curve, and Flat Curve with Friction

[Digitalx04]

Homework Statement

A car of mass M = 1200 kg traveling at 40.0 km/hour enters a banked turn covered with ice. The road is banked at an angle theta, and there is no friction between the road and the car's tires.

What is the radius r of the turn if $$\theta$$ = 20.0 degrees (assuming the car continues in uniform circular motion around the turn)?

The Attempt at a Solution

I believe that $$F_{c}$$ = $$F_{N}$$ sin ($$\theta$$) = m($$\frac{v^{2}}{r}$$)

Using this I solved for r, which is my missing variable and came up with:

r = $$\frac{v^{2}}{F_{N}sin\theta}$$

Using this formula I get
r = $$\frac{11.1^{2}}{9.8 sin 20}$$

but when I submitted this answer it told me the normal force is not equal to the weight of the car.

My questions are what is the $$F_{N}$$ value and am I missing another value in my equation?

 

[ideasrule]

Break down Fn into vertical and horizontal components. You already saw that the horizontal component provides the centripetal acceleration; what does the vertical component do?